An intuitive explanation of the Poisson equation?
Dec 8, 2023 · Poisson Equation: The Poisson equation, $$\nabla^2 u = f$$, describes how a scalar function (u) changes in response to a given "influence" represented by (f). It's like describing how a …
What are the differences between Heat equations and Poisson …
Jan 17, 2019 · Am fairly new into heat equations and wanted to have some clarifications. What are the distinguishing features between the heat equation and the Poisson equation?
Deriving Newton’s gravitational potential through Poisson’s equation ...
Nov 30, 2023 · 0 I am trying to derive Newton’s gravitational potential $\phi_N = -\frac {GM} {r}$ from Poisson’s equation $\Delta \phi_N = 4\pi G\rho$, where G is the gravitational constant, M is the mass …
newtonian gravity - Poisson equation and gravitational potential ...
Apr 28, 2024 · In Newtonian gravity, what is the difference between the Poisson equation $\Delta\phi =f$ and the expression $\phi = -GM/r$ for the gravitational potential $\phi$? Are both somewhat related?
When to use Poisson's equation in electrostatics
May 9, 2019 · Poisson's Equation is always applicable including in the absence of useful symmetries and offers some of its own tools for solution. You can often solve the associated differential …
Trouble with deriving the Euler-Poisson equation using Euler's approach
Dec 19, 2023 · 5 "A First Course in the Calculus of Variations" by Mark Kot, §2.2. Euler’s approach describes a method for deriving the Euler-Lagrange equation which I shall call "geometric". It is also …
Green Function for Poisson Equation Derivation
Jan 20, 2024 · I've read the Green function derivation for Poisson Equation (electrostatics) in this document. There are some points which are not clear for me. On page 10, the document starts with …
Fundamental solution of Poisson equation on the torus
Feb 22, 2024 · In order to obtain the fundamental solutions on the torus, we may extend the single Dirac delta to a Dirac comb with the periodicity of the torus, or consider the Poisson summation trick. While …
Still trying to understand gravitational potential and Poisson's equation?
Still trying to understand gravitational potential and Poisson's equation? Ask Question Asked 13 years, 9 months ago Modified 13 years, 9 months ago
Why Poisson's equation is important? - Physics Stack Exchange
The Poisson equation can be deduced by Newton's mechanics: $$\Delta \Phi =-4\pi G\sigma$$ Einstein tried to give a "Poisson's equation" that works with his theory. This equation seems to be impor...